Cheryl is training for a long bicycle ride. Jim will drive Cheryl back and her bicycle 60 miles from town, drop them off, and then drive back to town. Cheryl then will ride her bicycle back to town. On the way back to town, Jim will travel at 50 miles per hour and Cheryl will travel at 15 miles per hour. Cheryl plans on making two 15 minute rest stops. If Jim and Cheryl start back at the same time, how long, in hours and minutes, after Jim arrives in town Cheryl will arrive in town?
Jim takes 60/50 hrs = 72 minutes to drive back
Cheryl takes 4 hours = 240 minutes to ride and 30 minutes to rest = 270 min. in all.
270-72 = 198 min, or 3 hours and 18 min.
Hope Jim had a book...
To solve this problem, let's calculate the time it takes for Jim to drive back to town first.
The distance between Cheryl and the town is 60 miles, and Jim will travel this distance once, dropping Cheryl off. Therefore, Jim's total distance traveled is 60 miles.
Jim's speed is given as 50 miles per hour, so we can use the formula: time = distance / speed to find the time it takes for Jim to travel back to town.
Time = 60 miles / 50 miles per hour = 1.2 hours
Since there are 60 minutes in an hour, the decimal portion of the time represents the minutes. In this case, 0.2 hours is equal to 0.2 * 60 = 12 minutes.
So, it takes Jim 1 hour and 12 minutes to travel back to town.
Next, let's calculate the time it takes for Cheryl to ride her bicycle back to town.
The distance she needs to travel is 60 miles, and her speed is given as 15 miles per hour. We'll use the same formula, time = distance / speed, to find Cheryl's time.
Time = 60 miles / 15 miles per hour = 4 hours
Now, let's account for Cheryl's two 15-minute rest stops. Each rest stop will add 15 minutes to her total travel time.
2 rest stops * 15 minutes per rest stop = 30 minutes
So, Cheryl's total travel time, including the rest stops, is 4 hours + 30 minutes.
We can convert 4 hours to minutes by multiplying by 60: 4 hours * 60 minutes per hour = 240 minutes.
Total time = 240 minutes + 30 minutes = 270 minutes.
To convert this back to hours and minutes, we divide by 60.
Hours = 270 minutes / 60 minutes per hour = 4.5 hours
Since Cheryl will take 4 hours and 30 minutes to ride her bicycle back to town, she will arrive in town 4 hours and 30 minutes after Jim arrives.
To calculate the total time Cheryl will take to ride back to town, we need to consider two parts: the time Jim takes to drive back to town and the time Cheryl takes to ride her bicycle back.
Let's calculate the time it takes for Jim to drive back to town. Jim and Cheryl start at the same time, so by the time Jim reaches town, Cheryl will still be riding. The distance between Cheryl and Jim at that time will be 60 miles since Jim dropped Cheryl and her bicycle off there.
To calculate the time it takes for Jim to drive back to town, we use the formula:
Time = Distance / Speed.
Time = 60 miles / 50 miles per hour = 1.2 hours (or 1 hour and 12 minutes).
Now, let's calculate the time Cheryl will take to ride her bicycle back to town. Cheryl will ride at a speed of 15 miles per hour, and she will have two 15-minute rest stops.
The total distance Cheryl needs to travel back to town is also 60 miles since that's the distance Jim drove to drop her off.
To calculate the time Cheryl takes, we use the formula:
Time = Distance / Speed.
Time = 60 miles / 15 miles per hour = 4 hours.
Cheryl also takes two 15-minute rest stops.
So, Cheryl's total rest time will be 2 * 15 minutes = 30 minutes (0.5 hours).
Now, we add the driving time of Jim, Cheryl's riding time, and the rest time to find the total time Cheryl takes:
Total Time = Jim's driving time + Cheryl's riding time + Cheryl's rest time
= 1.2 hours + 4 hours + 0.5 hours
= 5.7 hours (or 5 hours and 42 minutes).
Therefore, Cheryl will arrive in town 5 hours and 42 minutes after Jim arrives.